OFFSET
0,2
COMMENTS
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) mod 10 = A131579(n+7).
G.f.: (1+21*x+8*x^2) / (1-x)^3 . - R. J. Mathar, Jul 01 2011
a(0)=1, a(1)=24, a(2)=77, a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Harvey P. Dale, May 02 2015
E.g.f.: (1 + 23*x + 15*x^2)*exp(x). - G. C. Greubel, Sep 20 2018
Sum_{n>=0} 1/a(n) = sqrt(2 + 3/sqrt(5) - sqrt(3 + 6/sqrt(5)))*Pi/(2*sqrt(6)) + sqrt(5)*log(phi)/4 + 5*log(5)/8 - 3*log(3)/4, where phi is the golden ratio (A001622). - Amiram Eldar, Sep 17 2023
MATHEMATICA
Table[(3n+1)(5n+1), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 24 , 77}, 50] (* Harvey P. Dale, Jul 16 2014 *)
PROG
(Magma) [(3*n+1)*(5*n+1): n in [0..40]]; // Vincenzo Librandi, Aug 07 2011
(PARI) a(n)=(3*n+1)*(5*n+1) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Oct 08 2008
STATUS
approved